Blender Boolean modifier: Difference behaves like union
You are trying to use a simple plane as boolean operand here - which is by definition not manifold (a manifold surface must be closed, since all its edges have to have two and only two faces). Behavior of booleans in this case is never really ensured…

Also, your 3DView only shows objects enabled for rendering, and your 'ObjA' object is disabled for rendering, so it's completely hidden from 3DView.

Other than that, I see no issue with this .blend, if there are please be more specific.